A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is #(pi)/4# and the angle between B and C is # (2pi)/3#. What is the area of the triangle?

1 Answer
Binayaka C.
Oct 31, 2016

Area of the triangle is #10.87(2dp) unit^2#

Explanation:

The angle between sides A and C is #/_b=pi/4=180/4=45^0#
The angle between sides B and C is #/_a=(2pi)/3=(2*180)/3=120^0#
The angle between sides A and B is #/_c=180-((45+120)=15^0#
Now we know sides #A=12 ; B=7# and their included angle #/_c=15^0#
So area of the triangle is #A_t=1/2*A*B*sinc= 1/2*12*7*sin15=10.87(2dp) unit^2# [Ans]

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